the characteristic of an individual by which it is treated as a unit or of a collection by which it is treated in terms of units

A Variable

A concept or characteristic that contains variation

Measurement

The assignment of numbers to indicate different values of a variable

Techniques or Instruments 3Measurement

Its purposes

to provide the basis for the results, conclusions, and significance of the research.

Measurement ltgt Invalid Research ?

to provide information about the variables that are being studied.

Measurement ltgt Variables

The way in which the numbers are used to describe something determines the amount of information that is communicatedA useful classification of this process is referred to as scales of measurement 4Measurement ScaleRatioOr Levels of MeasurementIntervalOrdinalNominalNumbers assigned to categoriesNNumbers ranked-orderedO

Frequency distribution It will indicates how often each score is obtained 6Measures of VariabilityRange Difference between the highest and lowest score(28-15) 13Standard Deviation Average distance of the scores from the meanSD4Symmetrical Distribution Positive SkewNegative Skew(mean, median, mode)(mode, median, mean)(mean, median, mode)Standard deviationsx individual scoresM meanN number of scores in group1s-1s2s0-2s 7CorrelationCorrelation Measure of relationship between two or more quantitative variablesCorrelation Coefficient A number between 1 and 1Which indicates the direction and strength of the relationship.Pearson Product-Moment Correlationr .45 8CorrelationSome examples 9Correlation vs. CausationReading LevelShoe size 10Measurement The basics

Construct a characteristic that cant be directly measured, e.g., intelligence

Operational definition a breakdown of what the elements are of that construct (e.g., verbal, quantitative, and analytical ability), or what that construct looks like in reality

Measure a numerical representation of part of the construct, e.g., items on an IQ test

Criterion-referenced tests tell you whether someone has achieved a certain level of performance, e.g., written drivers license test, and the test for this class!

18Inferential Statistics and Meta-Analysis 19Overview

What are inferential statistics?

Error, confidence intervals, statistical power

Hypothesis testing

Some of the basics

t-tests, chi-square, ANOVA

Correlation and regression analyses

Synthesizing multiple findings

The literature review

Meta-analysis

20What are inferential statistics?

Descriptive statistics

Show us how a single variable is distributed (frequency graphs)

Show us a picture of the relationship between two variables (correlations)

Inferential statistics

Allow us to get serious about checking hunches and hypotheses

Usually look at the strength of relationship between two or more variables

21Errors Getting the inference wrongExample Deciding to let/not let someone into graduate school on the basis of GRE scores 22Confidence intervals 1 margin of error for an individual score6895-2sd-1sd01sd2sd-3sd3sd99If we took a random individual from this population, there is a 95 chance that that persons score will fall between 2sd and 2sd. For IQ, thats a 95 chance of being between 70 and 130. 23Confidence intervals 2 meansDistribution of IQ scores in the normal population 95 of the individual scores lie between 70 and 130 (SD 15)708510011513055145If we took 100,000 groups of nine (9) people each, the mean IQs of those groups would be distributed like this ? i.e., 95 of the means would lie between 90 and 110 (SE 15/(SQRT(9)) 5)901001109510585115 24Example Intelligence (IQ)The normal population Mean 100A sample of 9 Michigan residents Mean 108708510011513055145Question Are Michigan folks unusually smart, or did we just accidentally end up with some particularly smart people in the sample? 25Hypothesis testing

We need to test two alternate hypotheses

No cause for alarm, America Michigan folks are just like other regular folks (i.e., the mean for this sample is not that off-the-wall)

The null hypothesis (H0)

Holy guacamole it looks like Michigan folks really are more brilliant than the rest (i.e., the mean for this sample is way out there)!!

The alternative hypothesis (H1)

26Is our group significantly different?Remember If we took 100,000 groups of nine (9) people each, the means of those groups would be distributed like this ? i.e., 95 of the means would lie between 90 and 110 (SE 15/(SQRT(9)) 5) OK, so is our mean of 108 unusually high? No! Because its inside the 95 range (90 to 110). gt We fail to reject the null hypothesis.9590100110 27What if we had a bigger sample?If we sample groups of 9 people, 95 of the means for those groups fall between IQ 90 and 1109590100110If we sample groups of 25 people, 95 of the means for those groups fall between IQ 94 and 106 (narrower)9594100106gt If our MI sample had been of 25 people with a mean IQ of 108, we could have been 95 certain that Michigan people were smarter (wed have had more power). But with a sample of only 9, we just couldnt be certain enough (even though it looked likely). 28Why do we want to be 95 sure?Consider the trade-off we make between errors 29Statistical vs. Practical Significance

Theres a flip-side to the statistical power issue with a big sample size, you can detect statistically significant effects that are trivial in the real world.

Example the Headstart program

Tens of thousands of children

A statistically significant effect gt many researchers claimed it worked!

The size of the change was trivial

30Choosing the right statistical test 1

Figure out which is/are your independent variable(s)

These are the predictors or the things that go on the X-axis of a graph

Figure out which is your dependent variable

This is usually the main thing you are interested in, the outcome, the thing that goes on the Y-axis of a graph

31Example IVs and DVs 32Choosing the right statistical test 2The type of test we use depends on the types of variables we have

Categorical (multiple categories)

Caucasian vs. African American vs. Hispanic vs.

Group 1 vs. 2 vs. 3

Continuous (interval ratio scales)

Age

Test scores

Shoe sizes

Dichotomous (just two options)

Male vs. female

Experimental group vs. control group

Pretest vs. posttest time

33Choosing the right test 3 34Synthesizing Studies Two Methods

The literature review

Reviewing, summarizing, and critiquing the main studies in a particular area, and drawing a conclusion about the strength of the evidence over multiple studies

Use when many of the best studies in the area are qualitative, or when there are not enough quant studies for a meta-analysis

Meta-analysis

A statistical technique for combining information about effect sizes to come to an overall conclusion about the strength of the evidence over multiple studies

Use when there are many quant studies out there already, some with conflicting results use to look for meta-effects (e.g., type of sample, type of intervention, etc)

What else could have accounted for the increase in math scores of students using the new hearing aid?

The students were better on the posttest because of the practice they got on the pretest testing/practice effect

The students tested happened to score a bit low on the day of the pretest, so the improvement was just the posttest moving closer to the average regression to the mean

39Rival explanations (contd)

The approach to teaching math changed between the pretest and the posttest history

The lowest-performing students were absent the day of the posttest mortality

Students of that age naturally get better at math at about that age maturation

Using the new hearing aid needed parental consent, and only those parents with a strong interest in their childs academic performance consented - selection

40Rival explanations (contd)

Students using the hearing aid felt this was special treatment, so tried harder Hawthorne effect

The hearing aid is novel, so the students feel excited and more motivated about listening (though the novelty wears off later on, after the posttest) novelty effect

The teacher expected to see better results among these students, and subconsciously tended to grade their answers more favorably researcher expectancy effect

41Simple experimental designsX treatment, C control, O test/measure

XO posttest only (no pretest)

OXO pretest and posttest

OXO/OCO pretest and posttest on both an experimental and a nonequivalent control group

Hard to rule out any of the rival explanations

Rules out selection and mortality

Rules out several rival explanations, but weaker because control group not equivalent

42Randomized designs

R OXO

OCO

R XO

CO

R OXO

OCO

XO

CO

randomly assigned experimental and control groups pre post

posttest only on randomly assigned exptal and control grps

Solomon four-group design two experimental and two control groups half pretested, all posttested

43What should a control group be?

Think of the practical question you need to answer with your research, e.g.,

Is this treatment/method better than nothing?

Is it better than what we are using now?

Consider the option of using a Placebo

In drug studies, this is the sugar pill

In experimental designs, it is an intervention that is not expected to affect the DV, but make sure the control group doesnt feel left out of the experimental group.

44Examples without control groups

Suppose you wanted to see if phonics training in kindergarten improved students ability to read in first grade

What would a posttest only design with no control group (XO) design entail (i.e., what ,whom, and when would you test)?

How about a pretest-posttest design with no control group (OXO) entail?

45Examples with control groups

Suppose you wanted to see if phonics training in kindergarten improved students ability to read in first grade

What would a pretest-posttest design with a control group (OXO/OCO) entail?

How about a posttest only design with a control (XO/CO)?

How would randomization help with each of the above? Is it practically feasible?

46The Solomon four-group design

Suppose you wanted to see if phonics training in kindergarten improved students ability to read in first grade

How would you set up a randomized Solomon four-group design?

R OXO

OCO

XO

CO

47Using multiple methodsWhat are the weaknesses of qual quant methods?

Quantitative

________________

________________

________________

________________

________________

________________

Qualitative

________________

________________

________________

________________

________________

________________

48Complementary multiplism

All research methods have weaknesses

Complementary multiplism (a.k.a. critical multiplism) is the practice of deliberately choosing complementary methods with different weaknesses, so that the strengths of one make up for the weaknesses of another

49Uses of mixed methods

To bring dry statistics alive

To dig into puzzling results and try to understand them better

To triangulate by getting multiple perspectives on one issue

If qual and quant data point in the same direction, you can be more certain that your results are robust

If they tell you something different, its time to dig again!

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